An empirical model of firm entry with endogenous product-type choices

Transcription

1 and An empirical model of firm entry with endogenous product-type choices, RAND Journal of Economics 31 Jan 2013

2 Introduction and Before : entry model, identical products In this paper : entry with simultaneous location choice Before or some other papers : complete info game In this paper : incomplete info game (greatly reduces computational burden) s : video retail industry location data firms differentiate to shield profit from competition more scope for product differentiation more market power (more entry)

3 Outline and 1 of the paper Data and 2 and weakness of the paper : Endogenized product-quality choice : Incomplete information on profits of the paper 3 for further research

4 and Section 1 of the paper

5 Setup and market m = 1, 2,..., M let s focus on one market m: (script m removed for ease of exposition) location l = 0, 1,..., L firm f = 1, 2,..., F decision d f = (d fl ) L l=0 {0, 1}L+1

6 Setup and payoff Π fl = X l β + ξ + h(γ.l, n) + ε fl X : observable market characteristics ξ : unobservable market characteristics, known to firms h() : effect of competition on profits; specified later Γ.l : interaction between l and 1 through L n = (n l ) L l=1 : number of firms at location l ε fl : idiosyncratic profitability of firm f at location l Π f 0 normalized to 0

7 Assumptions and Assumption (Independent symmetric private values) ε 1,..., ε F are private information to the players and are independently and identically distributed draws from the distribution G( ) Assumption (Additively separable competitors effects) h(γ.l, n) = L k=1 γ kln k Assumption (Distance bands) let d kl be the distance between location k and l. γ kl = γ k l = γ b if D b γ kl, γ k l < D b+1, where D b and D b+1 denote cutoffs that define a distance band.

8 Assumptions and Under distance bands b = 0, 1,..., B, with corresponding cutoff points D b and D b+1 where D 0 = 0, the resulting payoff function is given by Π fl = X l β + ξ + b γ bn bl + ε fl γ b : competitive effect in distance band b N bl = k Ib kl n k : number of firms in distance band b I b kl := I(d kl [D b, D b+1 )), I( ) : indicator function n k : number of firms at location k E := b N bl : total number of firms in the market

9 Conjectures and equilibrium and

10 Conjectures and equilibrium and Given the expected competitor distribution across market locations, firms calculate its expected profit at each location l : E(Π fl ) = X l β + ξ + b γ be(n bl ) + ε fl := E( Π fl ) + ε fl note that E(N bl ) = k Ib kl E(n k) Structure of the game : 1 firms decide whether or not to enter E determined 2 Given number of firms E, firms decide locations solve backward

11 Conjectures and equilibrium and Due to the symmetry of rival s types, firm f s perception of firm g s location strategy is the same for all competitors. Let θ 1 = (β, γ). Given ξ, X, E, θ 1, the probability that competitor g chooses location l is given by p gl (ξ, X, E, θ 1 ) = P(E( Π gl ) + ε gl > E( Π gk ) + ε gk k l, g f ) Expected number of competitors at location k is E(n k ) = (E 1)p gk E(N bl ) = k Ib kl E(n k) = k Ib kl (E 1)p gk + I(b = 0)

12 Conjectures and equilibrium and Assumption ε are i.i.d. draws from a type 1 extreme-value distribution with scale parameter normalized to one. By this assumption, there exists a closed-form formula for p gl : p gl = exp{e( Π gl )} L k=1 exp{e( Π gk )} Since types are symmetric, every firm has the same equilibrium conjecture of its competitors location choices : p g := (p gl ) L l=1 = p f = p := (p l )L l=1

13 Conjectures and equilibrium and A firm s vector of equilibrium conjectures over all locations l is defined by p l = = exp{e( Π l (X, p, E, θ 1 ))} L k=1 exp{e( Π k (X, p, E, θ 1 ))} j Ib jl p j } exp{x l β + γ 0 + (E 1) b γ b L k=1 exp{x kβ + γ 0 + (E 1) b γ b j Ib jk p j } for all l = 1,..., L

14 Conjectures and equilibrium and let s analyze E : In equilibrium, each entrant earns nonnegative profits in expectation, while any additional entrant would suffer losses. The probability of entry by a firm into a market involves a comparison of a weighted average of payoffs across locations to the normalized payoff of not entering.

15 Conjectures and equilibrium and Given the assumption of i.i.d. type 1 extreme-value profitability types, P(entry) = exp(ξ) L l=1 exp{e( Π l (X, p, E, θ 1 ))} 1 + exp(ξ) L l=1 exp{e( Π l (X, p, E, θ 1 ))} Since the probability of entry is identical across competitors, E = F P(entry) Ways to choose F : 50% enter the market, F = 50

16 : Econometric Specification and Assumption The expected number of entrants predicted by the model exactly equals the number of entrants observed in the data. With E being the observed number of entrants, by the entry probability equation, ( L ) ξ = ln E ln(f E) ln exp{e( Π l (X, p, E, θ 1 ))} l=1 Assumption ξ m are i.i.d. random draws from a Normal distribution with parameter θ 2 = (µ, σ) and independent of ε.

17 Likelihood and Data from market m = 1,..., M Each market is treated as an independent F m -player location game d m = (d1 m,..., d F m ) : vector of actions taken by F m players in market m The likelihood function is given by M L(θ 1, θ 2 ) = p θ1 (d m ξ m, X m, E m )g θ2 (ξ m X m, E m, F m ) m=1

18 Procedure and 1 initialize (θ 1, θ 2 ) 2 given (θ 1, θ 2 ), (X m ) M m=1, F, (Em ) M m=1, solve equilibrium conjecture equation for p m for each m separately 3 calculate ξ m with p m, (θ 1, θ 2 ), (X m ) M m=1, F, (Em ) M m=1 for each m 4 estimate (θ 1, θ 2 ) by maximizing likelihood function

19 Issues and initial value : a grid search over the parameter space likelihood maximization : Nelder-Mead optimization algorithm problematic when there are multiple equilibria : appendix proves uniqueness for two distance bands with four locations, simulation evidence suggests further result

20 Data description and video retail industry videotapes are standardized; main differentiation by store location isolated markets; no large city nearby, no metropolitan area exclude tourist regions locations by Census tracts

21 Data description and

22 Data description and

23 Data description and d 0 = 0.5 miles, d 1 = 3 miles

24 Data description and

25 and

26 and

27 Simulation and

28 Simulation and

29 and Section 2 and weakness of the paper

30 Previous Works and focused on tradeoff between demand and intensity of competition Early works on product quality differentiation : Hotelling(1929), Lancaster(1966,1979) (competition on characteristic space)

31 for Endogenized Choice and Empirically tractable model of competition on characteristic space (tractable for large L) Unisolated market : locations affect each other via distance

32 Empirical s and Firms differentiate to shield from competition More scope for product differentiation more market power(more entry) More disperse population less gain from differentiation(slightly more entry in total) The two offset each other in video retail industry data

33 Previous Works and Complete information game computational burden Limited number of locations Mazzeo(2002) : entry with product-quality choice, complete information game uses motel industry data, computation is burdensome with 3 locations

34 Incomplete Game and Introduce private information : idiosyncratic profitability sources: cost, intangible assets, customer service, inventory maintenance etc. As Rust(1994) notes : Bayesian Nash equilibrium conjectures are easy to derive Other works under information asymmetry : Aguirregabiria and Mira(2006), Pakes, Ostrovsky and Berry(2005), Pesendorfer and Schmidt-Dengler(2003)

35 Cost of Assumptions and Distance band approach : All locations with same distance band have the same impact two at the north one at the north and one at the south ε being i.i.d. type 1 extreme value distribution : idiosyncratic profitability uncorrelated across firms at a location, across location for a firm no spatial correlation

36 Possible Issues and When there are multiple equilibria : matching location probabilities to observed location choices is problematic uniqueness for general setting is only verified by simulation

37 and Section 3 for further research

38 Further research so far and entry game with multistore/multiproduct firms (Jia 2008) dynamic entry game timing game (Sweeting 2009) estimation with multiple equilibria (Aguirregabiria 2012 : identical product case) estimation in case of location heterogeneity (Aguirregabiria 2012)

39 Further research so far and estimation of demand system by quantity, price data of stores : Wang(2010) effect of other factors on entry decisions: regulation (Gowrisankaran and Krainer 2011), organizational structure (Takechi and Higashida 2012), managerial ability (Goldfarb and Xiao 2011)

40 and nonlinear effect of additional entrant relaxing distance band assumption investigation of conditions for unique equilibrium